PULSE-CODE MODULATION (pcm) refers to a system in which the standard values of a QUANTIZED WAVE (explained in the following paragraphs) are indicated by a series of coded pulses. When these pulses are decoded, they indicate the standard values of the original quantized wave. These codes may be binary, in which the symbol for each quantized element will consist of pulses and spaces: ternary, where the code for each element consists of any one of three distinct kinds of values (such as positive pulses, negative pulses, and spaces); or n-ary, in which the code for each element consists of nay number (n) of distinct values. This discussion will be based on the binary pcm system. All of the pulse-modulation systems discussed previously provide methods of converting analog wave shapes to digital wave shapes (pulses occurring at discrete intervals, some characteristic of which is varied as a continuous function of the analog wave). The entire range of amplitude (frequency or phase) values of the analog wave can be arbitrarily divided into a series of standard values. Each pulse of a pulse train [figure 2-48, view (B)] takes the standard value nearest its actual value when modulated. The modulating wave can be faithfully reproduced, as shown in views (C) and (D). The amplitude range has been divided into 5 standard values in view (C). Each pulse is given whatever standard value is nearest its actual instantaneous value. In view (D), the same amplitude range has been divided into 10 standard levels. The curve of view (D) is a much closer approximation of the modulating wave, view (A), than is the 5-level quantized curve in view (C). From this you should see that the greater the number of standard levels used, the more closely the quantized wave approximates the original. This is also made evident by the fact that an infinite number of standard levels exactly duplicates the conditions of nonquantization (the original analog waveform).
Figure 2-48A. - Quantization levels. MODULATION
Figure 2-48B. - Quantization levels. TIMING
Figure 2-48C. - Quantization levels. QUANTIZED 5-LEVEL
Figure 2-48D. - Quantization levels. QUANTIZED 10-LEVEL
Although the quantization curves of figure 2-48 are based on 5- and 10-level quantization, in actual practice the levels are usually established at some exponential value of 2, such as 4(22), 8(23), 16(24), 32(25) . . . N(2n). The reason for selecting levels at exponential values of 2 will become evident in the discussion of pcm. Quantized fm is similar in every way to quantized AM. That is, the range of frequency deviation is divided into a finite number of standard values of deviation. Each sampling pulse results in a deviation equal to the standard value nearest the actual deviation at the sampling instant. Similarly, for phase modulation, quantization establishes a set of standard values. Quantization is used mostly in amplitude- and frequency-modulated pulse systems.
Figure 2-49 shows the relationship between decimal numbers, binary numbers, and a pulse-code waveform that represents the numbers. The table is for a 16-level code; that is, 16 standard values of a quantized wave could be represented by these pulse groups. Only the presence or absence of the pulses are important. The next step up would be a 32-level code, with each decimal number represented by a series of five binary digits, rather than the four digits of figure 2-49. Six-digit groups would provide a 64-level code, seven digits a 128-level code, and so forth. Figure 2-50 shows the application of pulse-coded groups to the standard values of a quantized wave.
Figure 2-49. - Binary numbers and pulse-code equivalents.
Figure 2-50. - Pulse-code modulation of a quantized wave (128 bits).
In figure 2-50 the solid curve represents the unquantized values of a modulating sinusoid. The dashed curve is reconstructed from the quantized values taken at the sampling interval and shows a very close agreement with the original curve. Figure 2-51 is identical to figure 2-50 except that the sampling interval is four times as great and the reconstructed curve is not faithful to the original. As previously stated, the sampling rate of a pulsed system must be at least twice the highest modulating frequency to get a usable reconstructed modulation curve. At the sampling rate of figure 2-50 and with a 4-element binary code, 128 bits (presence or absence of pulses) must be transmitted for each cycle of the modulating frequency. At the sampling rate of figure 2-51, only 32 bits are required; at the minimum sampling rate, only 8 bits are required.
Figure 2-51. - Pulse-code modulation of a quantized wave (32 bits).
As a matter of convenience, especially to simplify the demodulation of pcm, the pulse trains actually transmitted are reversed from those shown in figures 2-49, 2-50, and 2-51; that is, the pulse with the lowest binary value (least significant digit) is transmitted first and the succeeding pulses have increasing binary values up to the code limit (most significant digit). Pulse coding can be performed in a number of ways using conventional circuitry or by means of special cathode ray coding tubes. One form of coding circuit is shown in figure 2-52. In this case, the pulse samples are applied to a holding circuit (a capacitor which stores pulse amplitude information) and the modulator converts pam to pdm. The pdm pulses are then used to gate the output of a precision pulse generator that controls the number of pulses applied to a binary counter. The duration of the gate pulse is not necessarily an integral number of the repetition pulses from the precisely timed clock-pulse generator. Therefore, the clock pulses gated into the binary counter by the pdm pulse may be a number of pulses plus the leading edge of an additional pulse. This "partial" pulse may have sufficient duration to trigger the counter, or it may not. The counter thus responds only to integral numbers, effectively quantizing the signal while, at the same time, encoding it. Each bistable stage of the counter stores ZERO or a ONE for each binary digit it represents (binary 1110 or decimal 14 is shown in figure 2-52). An electronic commutator samples the 20, 21, 22, and 23 digit positions in sequence and transmits a mark or space bit (pulse or no pulse) in accordance with the state of each counter stage. The holding circuit is always discharged and reset to zero before initiation of the sequence for the next pulse sample.
Figure 2-52. - Block diagram of quantizer and pcm coder.
The pcm demodulator will reproduce the correct standard amplitude represented by the pulse-code group. However, it will reproduce the correct standard only if it is able to recognize correctly the presence or absence of pulses in each position. For this reason, noise introduces no error at all if the signal-to-noise ration is such that the largest peaks of noise are not mistaken for pulses. When the noise is random (circuit and tube noise), the probability of the appearance of a noise peak comparable in amplitude to the pulses can be determined. This probability can be determined mathematically for any ration of signal-to-average-noise power. When this is done for 105 pulses per second, the approximate error rate for three values of signal power to average noise power is:
17 dB - 10 errors per second
Above a threshold of signal-to-noise ration of approximately 20 dB, virtually no errors occur. In all other systems of modulation, even with signal-to-noise ratios as high as 60 dB, the noise will have some effect. Moreover, the pcm signal can be retransmitted, as in a multiple relay link system, as many times as desired, without the introduction of additional noise effects; that is, noise is not cumulative at relay stations as it is with other modulation systems.
The system does, of course, have some distortion introduced by quantizing the signal. Both the standard values selected and the sampling interval tend to make the reconstructed wave depart from the original. This distortion, called QUANTIZING NOISE, is initially introduced at the quantizing and coding modulator and remains fixed throughout the transmission and retransmission processes. Its magnitude can be reduced by making the standard quantizing levels closer together. The relationship of the quantizing noise to the number of digits in the binary code is given by the following standard relationship:
n is the number of digits in the binary code
Thus, with the 4-digit code of figure 2-50 and 2-51, the quantizing noise will be about 35 dB weaker than the peak signal which the channel will accommodate.
The advantages of pcm are two-fold. First, noise interference is almost completely eliminated when the pulse signals exceed noise levels by a value of 20 dB or more. Second, the signal may be received and retransmitted as many times as may be desired without introducing distortion into the signal.
Q.27 Pulse-code modulation requires the use of approximations of value that are
obtained by what process?